We present a novel method for representing and evolving objects of arbitrary dimension. The method, called the Vector Distance Function (VDF) method, uses the vector that connects any point in space to its closest point on the object. It can deal with smooth manifolds with and without boundaries and with shapes of diierent dimensions. It can be used to evolve such objects according to a variety...

Thorsten Emmerich,1 Armin Bunde,1 Shlomo Havlin,2 Guanliang Li,3 and Daqing Li4 1Institut für Theoretische Physik, Justus-Liebig-Universität Giessen, 35392 Giessen, Germany 2Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel 3Center for Polymer Studies, Department of Physics, Boston University, Boston, Massachusetts 02215, USA 4School of Reliability and Systems Engineering, Bei...

This work demonstrates that the distance measuring the likelihood of the graphs of two functions, usually referred as Hausdor distance between functions and widely used in function approximation tasks and signal processing, can be calculated e ciently using grey scale morphological operations even in the case of noncontinuous (discrete as well as nondiscrete) functions. Also we have presented a...

A subset of the finite dimensional hypercube is said to be equilateral if the distance of any two distinct points equals a fixed value. The equilateral dimension of the hypercube is defined as the maximal size of its equilateral subsets. We study asymptotic bounds on the latter quantity considered as a function of two variables, namely dimension and distance. lorenz minder, thomas sauerwald and...

Abstract— binary linear error correcting codes represented by two code families Kronecker products sum are considered. The dimension and distance of new code is investigated. Upper and lower bounds of distance are obtained. Some examples are given. It is shown that some classic constructions are the private cases of considered one. The subclass of codes with equal lower and upper distance bound...

Since the seminal paper of Kötter and Kschischang [20] there is a still growing interest in subspace codes, which are sets of subspaces of the Fq-vector space F n q . If all subspaces, which play the role of the codewords, have the same dimension, say k, then one speaks of constant dimension codes. The most commonly used distance measures for subspace codes, motivated by an information-theoreti...

We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, connectedness, compactness and completeness. The construction of the distance is related to the DuistermaatHeckman measure and the Hausdorff metric. While the moduli space, its topology and metric, may be constructed in any di...

The main result of this paper is the following. Given countably many multivariate polynomials with rational coefficients and maximum degree d, we construct a compact set E ⊂ Rn of Hausdorff dimension n/d which does not contain finite point configurations corresponding to the zero sets of the given polynomials. Given a set E ⊂ Rn, we study the angles determined by three points of E. The main res...